Barotropic and Baroclinic Instabilities in Jupiter's Zonal Flow

Citation

Pollard, David (1979) Barotropic and Baroclinic Instabilities in Jupiter's Zonal Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/r49b-st82. https://resolver.caltech.edu/CaltechETD:etd-09082006-081730

Abstract

The barotropic and baroclinic stability of Jupiter's zonal jets is investigated using a two-layer quasi-geostrophic model. Each layer is of constant density with the upper layer representing the cloudy levels of Jupiter's atmosphere above p ~ 5 bars containing the zonal jets u̅(y), and a much deeper lower layer in which u̅ = 0; [roughly consistent with Gierasch (Icarus, 29 1976)]. Since Jupiter's vertical structure associated with the zonal jets is unknown at these levels, this model attempts to include the effects of baroclinicity and deep lower layer inertia with as few free vertical-structure parameters as possible (i.e., the upper layer Rossby radius of deformation Lr and the ratio of the upper layer to lower layer thickness δ).

Given that δ << 1 for Jupiter, the linearized dynamical equations can be expanded in powers of δ and also of δ¹/². These expansions naturally categorize the possible disturbances into three types; barotropic (BTU) modes, almost entirely confined to the upper layer with potentially 0(1) growth rates; baroclinic (BC) modes, which depend on interactions between the two layers and can only have 0(δ) growth rates; and barotropic (BTL) modes of the lower fluid with 0(δ¹/²) growth rates. Some results for the BC modes are presented and compared to results of a continuously stratified model developed in the appendix, but mostly the faster growing BTU modes are investigated for two analytically tractable velocity profiles [sech²(y) and tanh (y), following Lipps (e.g., J. Fluid Mech., 21, 1965)]. The x-wavelengths, phase speeds, growth rates, horizontal morphologies and the latitudinal forms of the eddy transports u'v' of the fastest growing disturbances depend on u̅(y) and on the model parameter Lr.

In mid 1979, two Voyager spacecraft may return images of cloud motions around the p ~ 1 bar level, yielding u̅(y) and eddy u'(x,y,t) and v'(x,y,t). Models of the present type are necessary to form a basis for interpreting such data, to initially identify and categorize the types of disturbances, at least until more is known of the vertical structure associated with the zonal jets. Best-fitting of the model's results to corresponding Voyager data may constrain Lr and δ, two basic vertical-structure parameters. In the last section, the theoretical results for BTU modes listed above are summarized and presented in forms most suitable for comparisons with the anticipated data.

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